Phylogenetic comparative methods are a set of statistical methods that model the evolutionary history of species, especially in the context where one has data on certain traits of related extant species that have evolved over a phylogenetic tree in accordance to an underlying stochastic process.  This thesis presents a Hessian-based closed-form asymptotic confidence region that covers a wide family of Gaussian continuous-trait evolution models; the result has been implemented in an R package. Also, some analyses have been done on the simpler Brownian Motion and Ornstein-Uhlenbeck process cases; and this leads to novel exact confidence regions for the Brownian Motion’s parameters and a closed-form ’partial’ unbiased estimator for the Ornstein-Uhlenbeck process’ varaince-covariance matrix when other parameters are given.  The thesis contains two papers. Paper I is an applied work that uses discrete-trait speciation and extinction model to investigate early spread of COVID-19; it shows that it is possible to detect statistical signals of inter-continental spread of the virus from a very noisy world-wide phylogeny. Paper II is a more mathematical work that derived the closed-form formulae for the Hessian matrix of a wide family of Gaussian-process-based multivariate continuous-trait PCM models; accompanying with the Paper I have developed an R package called glinvci, publicly available on The Comprehensive R Archive Network (CRAN), that can compute Hessian-based confidence regions for these models while at the same time allowing users to have missing data and multiple evolutionary regimes. / <p><strong>Funding:</strong> Vetenskapsrådet [Grant 2017-04951] and STIMA.</p><p>2024-04-05: Series have been corrected in the e-version</p><p></p>

Gymnasieelevers förståelse av naturligt urval och fylogenetiska träd har undersökts genom en enkätundersökning med 223 elever på fyra gymnasieskolor i Sverige. Resultatet från studien visar att elever oftare svarar rätt på flervalsfrågor med evolutionära träd än på frågor som behandlar naturligt urval. Det skulle kunna vara för att de frågor (och svar) som tar upp naturligt urval har mer text, där den relevanta informationen måste kunna tas ut först från frågan och sedan från svarsalternativen för att kunna välja det rätta alternativet. Resultatet visar även att det inte finns något samband mellan elevernas förståelse av evolutionära träd och naturligt urval. Eleverna kan alltså förstå det ena (evolutionära träd) men behöver inte nödvändigtvis förstå det andra (naturligt urval) och vice versa. / High school students understanding of natural selection and phylogenetic trees has been tested through a survey of 223 pupils in four upper secondary schools in Sweden. The results of the study show that students more often choose the correct answer on multiple choice questions with evolutionary trees than on questions that address natural selection. One reason for this could be that the questions (and answers) that address natural selection have more text, where the students must be able to take out the relevant information first from the question and then from the answers, in order to be able to choose the correct answer. The result also shows that there is no connection between the students understanding of evolutionary trees and natural selection. The pupils can thus understand one (evolutionary trees) but do not necessarily need to understand the other (natural selection) and vice versa.